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Fig. 5.16 A model of a two-layer disk that accounts for the spectrum observed in Fig. 5.15. The thickness of the disk increases with distance from the star. The stellar radiation is absorbed by the dust in the disk's outer layer, whose temperature rises higher than that of the gas (After Chiang and Goldreich, 1997)

Fig. 5.16 A model of a two-layer disk that accounts for the spectrum observed in Fig. 5.15. The thickness of the disk increases with distance from the star. The stellar radiation is absorbed by the dust in the disk's outer layer, whose temperature rises higher than that of the gas (After Chiang and Goldreich, 1997)

5.2.6 Later Stages of Stellar Evolution: Evolution Towards the Main Sequence

In a first approach, the evolution of the internal structure of a star beyond the T-Tauri phase may be described by means of four fundamental equations (Acker, 2005):

(1) the perfect gas equation:

R pT

where P is the pressure, R the perfect gas constant, p the density, T the temperature, and | the mean molecular weight;

(2) conservation of mass:

(3) hydrostatic equilibrium:

dr r2

where G is the gravitational constant;

(4) conservation of energy:

dr where e is the energy (of nuclear origin).

The energy is transported towards the outer layers by convection or by radiation. In the case of radiative transfer, the energy-transport depends on the opacity of the medium, which, in turn, depends on its chemical composition (gas and dust). Under the condition of LTE (local thermodynamic equilibrium, see Sect. 4.4.2.2.) the radiation, assumed to be isotropic, is given by Planck's Law. The luminosity, L, as a function of radius is given by:

w 3 pK dr an expression in which k is the opacity and o Stefan's constant. Stability of the star implies a balance between the gravitational force that induces collapse, and the radiation pressure that tends to make the star expand. The radiation pressure Prad is expressed as:

Equilibrium cannot be maintained if the radiation pressure is less than the total pressure P — Pgas + Prad. By using the hydrostatic equilibrium law, it may be shown that this condition implies that the star's luminosity remains less than a value known as the Eddington luminosity:

4ncGM

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